A flexing-contact-type gear drive typically consists of a rigid circular internal gear, a flexible external gear which has 2n (n being a positive integer) less teeth than the internal gear and which is disposed inside the internal gear and flexed into an elliptical shape so as to mesh with the internal gear at two places, and wave generator fitted inside the external gear for flexing it. The axial length of the flexing external gear is set approximately equal to the diameter thereof.
The basic tooth profile for the gears of a flexing contact gear drive is linear (see U.S. Pat. No. 2,906,143). On the other hand, an involute tooth profile has also been proposed by one of the inventors of the present invention (see Japanese Patent Publication No. SHO 55-41171). However, where the linear or the involute tooth profile is adopted as that of each of the internal and external gears, the addendum faces of the gears cannot be continuously meshed with each other.
For increasing load capacity the inventor of the present invention proposed a system using as the basis for the tooth face profile the curve obtained by similarity transforming the locus of motion at a reduction ratio of 1/2 over a prescribe range from the meshing limit point on the locus of motion based on the rack approximation of the tooth of the external gear relative to the internal gear determined by the shape of the wave generator (Japanese Patent Laid Open No. SHO 63-115923).
However, the each of the above inventions is directed to a flexing contact type gear drive of the type having a cylindrical flexible external gear called as a flat type or a pan cake type. Therefore, the change in deflection along an axis of the flexible gear caused by coning when the cup-shaped flexible external gear is employed, is not taken into consideration. Hence, the proposed tooth profiles function properly at a specific section of tooth trace (for example, at a section of non deviation), but at the other sections, defects such as non contact of the teeth, tooth interference and the like may occur. As mentioned above, although the tooth profiles of the above inventions are effective for a case where the cylindrical flexible external gear is employed, they are not applicable for a case where the cup-shaped flexible external gear is employed.
In addition, where a cup-shaped flexible external gear is reduced in its axial length for the purpose of volume reduction thereof, a degree of coning of the flexible external gear becomes larger, and so the defects caused by using the tooth profiles of the above inventions become remarkable.
In terms of these defects, there has been a demand for an improvement of the tooth profiles. Inventions disclosed in Japanese Patent Laid Open Nos. SHO 62-75153 and HEI 2-62461 are directed to an improvement for avoiding the above defects. In these methods, however, it is required to apply special additional-processing such as crowing, relieving and the like on teeth. Moreover, no consideration is made in the above publications on the reduction in axial length of a cup-shaped flexible external gear.
An object of the present invention is to provide a flexing contact type gear drive which, without requiring special additional-processing such as crowing, relieving and the like, is capable of realizing a wider range of meshing of the teeth along the whole tooth trace direction of a cup-shaped external gear without interference, and at the same time which is easily machined and is capable of reducing an axial length of the cup-shaped flexible external gear.